Details

sample286.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	9
1	74	9
2	160	9
3	483	9
4	1845	9
5	5001	9

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(* (* 2.0 PI) u2)
0.4b	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp` `add-cbrt-cube`
12×	`pow1`
11×	`times-frac`
8×	`associate-r`
6×	`pow-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-to-exp` `pow-unpow`
2×	`unpow-prod-down` `pow-pow` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

29.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
2.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(* (* 2.0 PI) u2)
13.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

series1.5s

Counts

4 → 12

Calls

4 calls:

462.0ms	(+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)
264.0ms	(pow (* -2.0 (log u1)) 0.5)
32.0ms	(* (* 2.0 PI) u2)
694.0ms	(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	523	772
1	2229	700
2	5001	697

prune356.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.3b	(* (* 2.0 PI) u2)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
9×	`prod-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow`
1×	`+-commutative` `unpow-prod-down` `fma-def` `frac-2neg` `flip3-+` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

12.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
2.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
6.0ms	(* (* 2.0 PI) u2)

series1.5s

Counts

4 → 12

Calls

4 calls:

466.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (* (* 2.0 PI) u2))) 0.5)
268.0ms	(pow (* -2.0 (log u1)) 0.5)
696.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
36.0ms	(* (* 2.0 PI) u2)

simplify57.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	472	641
1	2101	569
2	5002	564

prune296.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (expm1 (log1p (* (* 2.0 PI) u2))))) 0.5)
0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
0.3b	(* (* 2.0 PI) u2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
9×	`prod-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-unpow` `times-frac` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `cos-diff` `pow-to-exp` `associate-+l+` `pow-pow` `expm1-udef`
1×	`+-commutative` `distribute-rgt-in` `unpow-prod-down` `fma-def` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `associate-/l` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

8.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (expm1 (log1p (* (* 2.0 PI) u2))))) 0.5)
3.0ms	(pow (* -2.0 (log u1)) 0.5)
4.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
6.0ms	(* (* 2.0 PI) u2)

series1.5s

Counts

4 → 12

Calls

4 calls:

523.0ms	(+ (* (/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0) (cos (expm1 (log1p (* (* 2.0 PI) u2))))) 0.5)
271.0ms	(pow (* -2.0 (log u1)) 0.5)
697.0ms	(/ (* 1.0 (pow (* -2.0 (log u1)) 0.5)) 6.0)
37.0ms	(* (* 2.0 PI) u2)

simplify62.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	494	707
1	2172	619
2	5002	609

prune341.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* -2.0 (log u1)) 0.5)
0.3b	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
0.3b	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
0.3b	(* (* 2.0 PI) u2)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log`
24×	`associate-/r*`
17×	`unpow-prod-down` `sqr-pow`
16×	`add-cbrt-cube`
13×	`div-exp`
12×	`pow1`
6×	`pow-exp` `prod-exp` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `cbrt-unprod`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`associate-l` `associate-/r/` `*-commutative`

Counts

4 → 178

Calls

4 calls:

2.0ms	(pow (* -2.0 (log u1)) 0.5)
7.0ms	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
3.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
6.0ms	(* (* 2.0 PI) u2)

series1.8s

Counts

4 → 12

Calls

4 calls:

270.0ms	(pow (* -2.0 (log u1)) 0.5)
720.0ms	(/ 1.0 (/ 6.0 (pow (* -2.0 (log u1)) 0.5)))
780.0ms	(/ 6.0 (pow (* -2.0 (log u1)) 0.5))
33.0ms	(* (* 2.0 PI) u2)

simplify89.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	695	1598
1	3034	1524
2	5002	1524

prune762.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes276.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12

end0.0ms

sample936.0ms

Algorithm

intervals

Results

662.0ms	8000×	body	80	valid
123.0ms	8000×	pre	80	true